NEW YORK, Feb 21 (Reuters) - Investment firm G Asset Management said on Friday that it had offered to buy a 51 percent stake in either Barnes & Noble Inc or in the bookseller's Nook digital business.

The little known firm said the proposal for Barnes & Noble as a whole would be for $22 per share, which would value the top U.S. bookstore chain at $1.32 billion. It follows an earlier proposal in November for $20 per share, its second.

G Asset, which not did detail how it would finance a deal, also made an alternative offer to buy Nook for $5 per share, saying spinning off the digital books and device business would create "substantial shareholder value."

The latest offer for the whole company would value Barnes & Noble at $1.32 billion, while the proposal for Nook would value that unit at about $300 million.

The firm has previously pressed the company to spin off its Nook unit from Barnes & Noble's bookstore and college units.

Michael Glickstein, G Asset's Chief Investment Officer, and the only person listed on the firm's website, did not immediately return a request for comment.

Barnes & Noble shares were up 5.8 percent at $17.75 in afternoon trading after going as high as $19.12 after the news was released, suggesting Wall Street analysts were doubtful a deal would get done.

A Barnes & Noble spokeswoman declined to comment beyond confirming that the company had received G Asset's offer.

The original Nook device was launched in 2009 to help Barnes & Noble fend off Amazon.com Inc and allowed the retailer to win as much as 27 percent of the U.S. e-books market.

But the company lost hundreds of millions of dollars trying to keep pace with deep-pocketed rivals such as Amazon, Apple Inc and Google Inc. It has scaled back its Nook business and focusing more on content and software.

Two years ago, Microsoft Corp invested $300 million in the Nook unit for a 17.6 percent stake, valuing the division at $1.7 billion. In late 2012, Pearson PLC took a 5 percent stake in Nook for $89.5 million.